Related papers: FMint-SDE: A Multimodal Foundation Model for Accel…
We outline the basic ideas and techniques underpinning the simulation of stochastic differential equations. In particular we focus on strong simulation and its context. We also provide illustratory examples and sample matlab algorithms for…
Ordinary differential equations (ODEs) describe dynamical systems evolving deterministically in continuous time. Accurate data-driven modeling of systems as ODEs, a central problem across the natural sciences, remains challenging,…
We propose an accurate data-driven numerical scheme to solve Stochastic Differential Equations (SDEs), by taking large time steps. The SDE discretization is built up by means of a polynomial chaos expansion method, on the basis of…
Modeling stochastic differential equations (SDEs) is crucial for understanding complex dynamical systems in various scientific fields. Recent methods often employ neural network-based models, which typically represent SDEs through a…
Multi-fidelity surrogate learning is important for physical simulation related applications in that it avoids running numerical solvers from scratch, which is known to be costly, and it uses multi-fidelity examples for training and greatly…
We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and…
Solving high-dimensional partial differential equations (PDEs) is a critical challenge where modern data-driven solvers often lack reliability and rigorous error guarantees. We introduce Simulation-Calibrated Scientific Machine Learning…
Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…
Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…
Partial differential equations (PDEs) govern a wide range of physical systems, and recent multimodal foundation models have shown promise for learning PDE solution operators across diverse equation families. However, existing multi-operator…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…
In this paper, we address the issue of modeling and estimating changes in the state of the spatio-temporal dynamical systems based on a sequence of observations like video frames. Traditional numerical simulation systems depend largely on…
Fractional-order differential equations (FDEs) enhance traditional differential equations by extending the order of differential operators from integers to real numbers, offering greater flexibility in modeling complex dynamical systems…
High-dimensional recordings of dynamical processes are often characterized by a much smaller set of effective variables, evolving on low-dimensional manifolds. Identifying these latent dynamics requires solving two intertwined problems:…
We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surrogate models of the fine scale dynamics. We approximate the…
The accurate representation of numerous physical, chemical, and biological processes relies heavily on differential equations (DEs), particularly nonlinear differential equations (NDEs). While understanding these complex systems…
Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While…
The development of data-driven approaches for solving differential equations has been followed by a plethora of applications in science and engineering across a multitude of disciplines and remains a central focus of active scientific…
Moment estimation for stochastic differential equations (SDEs) is fundamental to the formal reasoning and verification of stochastic dynamical systems, yet remains challenging and is rarely available in closed form. In this paper, we study…
Optimizing robotic action parameters is a significant challenge for manipulation tasks that demand high levels of precision and generalization. Using a model-based approach, the robot must quickly reason about the outcomes of different…